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Solving integrals/ x^3-9x

Integral of x^3-9x dx

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The solution

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∫−13(x3−9x) dx\int\limits_{-1}^{3} \left(x^{3} - 9 x\right)\, dx 
Integral(x^3 - 9*x, (x, -1, 3))
Detail solution

  1. Integrate term-by-term:

    1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

      ∫x3 dx=x44\int x^{3}\, dx = \frac{x^{4}}{4}

    1. The integral of a constant times a function is the constant times the integral of the function:

      ∫(−9x) dx=−9∫x dx\int \left(- 9 x\right)\, dx = - 9 \int x\, dx

      1. The integral of xnx^{n} is xn+1n+1\frac{x^{n + 1}}{n + 1} when n≠−1n \neq -1:

        ∫x dx=x22\int x\, dx = \frac{x^{2}}{2}

      So, the result is: −9x22- \frac{9 x^{2}}{2}

    The result is: x44−9x22\frac{x^{4}}{4} - \frac{9 x^{2}}{2}

  2. Now simplify:

    x2(x2−18)4\frac{x^{2} \left(x^{2} - 18\right)}{4}

  3. Add the constant of integration:

    x2(x2−18)4+constant\frac{x^{2} \left(x^{2} - 18\right)}{4}+ \mathrm{constant}

The answer is:

x2(x2−18)4+constant\frac{x^{2} \left(x^{2} - 18\right)}{4}+ \mathrm{constant}

The answer (Indefinite) [src] 
  /                             
 |                        2    4
 | / 3      \          9*x    x 
 | \x  - 9*x/ dx = C - ---- + --
 |                      2     4 
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∫(x3−9x) dx=C+x44−9x22\int \left(x^{3} - 9 x\right)\, dx = C + \frac{x^{4}}{4} - \frac{9 x^{2}}{2}
Simplify
The graph
-1.0-0.53.00.00.51.01.52.02.5-5050
Plot the graph f(x)
The answer [src] 
-16
−16-16 
=
= 
-16
−16-16 
-16
Numerical answer [src] 
-16.0
-16.0

    Use the examples entering the upper and lower limits of integration.

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